<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.9.1"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Eigen-unsupported: MatrixPower.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
  $(document).ready(function() { init_search(); });
/* @license-end */
</script>
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
    jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="eigendoxy.css" rel="stylesheet" type="text/css">
<!--  -->
<script type="text/javascript" src="eigen_navtree_hacks.js"></script>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
 <tbody>
 <tr style="height: 56px;">
  <td id="projectlogo"><img alt="Logo" src="Eigen_Silly_Professor_64x64.png"/></td>
  <td id="projectalign" style="padding-left: 0.5em;">
   <div id="projectname"><a href="http://eigen.tuxfamily.org">Eigen-unsupported</a>
   &#160;<span id="projectnumber">3.4.90 (git rev 67eeba6e720c5745abc77ae6c92ce0a44aa7b7ae)</span>
   </div>
  </td>
   <td>        <div id="MSearchBox" class="MSearchBoxInactive">
        <span class="left">
          <img id="MSearchSelect" src="search/mag_sel.svg"
               onmouseover="return searchBox.OnSearchSelectShow()"
               onmouseout="return searchBox.OnSearchSelectHide()"
               alt=""/>
          <input type="text" id="MSearchField" value="Search" accesskey="S"
               onfocus="searchBox.OnSearchFieldFocus(true)" 
               onblur="searchBox.OnSearchFieldFocus(false)" 
               onkeyup="searchBox.OnSearchFieldChange(event)"/>
          </span><span class="right">
            <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.svg" alt=""/></a>
          </span>
        </div>
</td>
 </tr>
 </tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.1 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'Search','.html');
/* @license-end */
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
  <div id="nav-tree">
    <div id="nav-tree-contents">
      <div id="nav-sync" class="sync"></div>
    </div>
  </div>
  <div id="splitbar" style="-moz-user-select:none;" 
       class="ui-resizable-handle">
  </div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('MatrixPower_8h_source.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div class="header">
  <div class="headertitle">
<div class="title">MatrixPower.h</div>  </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2012, 2013 Chen-Pang He &lt;jdh8@ms63.hinet.net&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_MATRIX_POWER</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_MATRIX_POWER</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt; <span class="keyword">class </span>MatrixPower;</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment">/* TODO This class is only used by MatrixPower, so it should be nested</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment"> * into MatrixPower, like MatrixPower::ReturnValue. However, my</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="comment"> * compiler complained about unused template parameter in the</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment"> * following declaration in namespace internal.</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment"> * template&lt;typename MatrixType&gt;</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment"> * struct traits&lt;MatrixPower&lt;MatrixType&gt;::ReturnValue&gt;;</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerParenthesesReturnValue.html">   41</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixPowerParenthesesReturnValue.html">MatrixPowerParenthesesReturnValue</a> : <span class="keyword">public</span> ReturnByValue&lt; MatrixPowerParenthesesReturnValue&lt;MatrixType&gt; &gt;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;{</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerParenthesesReturnValue.html#ae3a02d943a31427a6dc8c1f60f3367d7">   52</a></span>&#160;    <a class="code" href="classEigen_1_1MatrixPowerParenthesesReturnValue.html#ae3a02d943a31427a6dc8c1f60f3367d7">MatrixPowerParenthesesReturnValue</a>(<a class="code" href="classEigen_1_1MatrixPower.html">MatrixPower&lt;MatrixType&gt;</a>&amp; pow, RealScalar p) : m_pow(pow), m_p(p)</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    { }</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerParenthesesReturnValue.html#af91430ff248b714158cfba4301cc0e2b">   61</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixPowerParenthesesReturnValue.html#af91430ff248b714158cfba4301cc0e2b">evalTo</a>(ResultType&amp; result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="keyword">    </span>{ m_pow.compute(result, m_p); }</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_pow.rows(); }</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_pow.cols(); }</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    MatrixPower&lt;MatrixType&gt;&amp; m_pow;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <span class="keyword">const</span> RealScalar m_p;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;};</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerAtomic.html">   88</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixPowerAtomic.html">MatrixPowerAtomic</a> : internal::noncopyable</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;{</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;      RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    };</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keyword">typedef</span> std::complex&lt;RealScalar&gt; ComplexScalar;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    <span class="keyword">typedef</span> <a class="codeRef" href="../classEigen_1_1Block.html">Block&lt;MatrixType,Dynamic,Dynamic&gt;</a> <a class="codeRef" href="../classEigen_1_1Block.html">ResultType</a>;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    <span class="keyword">const</span> MatrixType&amp; m_A;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    RealScalar m_p;</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="keywordtype">void</span> computePade(<span class="keywordtype">int</span> degree, <span class="keyword">const</span> MatrixType&amp; IminusT, <a class="codeRef" href="../classEigen_1_1Block.html">ResultType</a>&amp; res) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <span class="keywordtype">void</span> compute2x2(<a class="codeRef" href="../classEigen_1_1Block.html">ResultType</a>&amp; res, RealScalar p) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    <span class="keywordtype">void</span> computeBig(<a class="codeRef" href="../classEigen_1_1Block.html">ResultType</a>&amp; res) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">int</span> getPadeDegree(<span class="keywordtype">float</span> normIminusT);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">int</span> getPadeDegree(<span class="keywordtype">double</span> normIminusT);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">int</span> getPadeDegree(<span class="keywordtype">long</span> <span class="keywordtype">double</span> normIminusT);</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="keyword">static</span> ComplexScalar computeSuperDiag(<span class="keyword">const</span> ComplexScalar&amp;, <span class="keyword">const</span> ComplexScalar&amp;, RealScalar p);</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keyword">static</span> RealScalar computeSuperDiag(RealScalar, RealScalar, RealScalar p);</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160; </div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <a class="code" href="classEigen_1_1MatrixPowerAtomic.html#ac0ec5f8d6c203cd9b53e2c95e01037d4">MatrixPowerAtomic</a>(<span class="keyword">const</span> MatrixType&amp; T, RealScalar p);</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    </div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixPowerAtomic.html#ac3cdfb54a5b60079d068784534cbc174">compute</a>(<a class="codeRef" href="../classEigen_1_1Block.html">ResultType</a>&amp; res) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;};</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160; </div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00136"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerAtomic.html#ac0ec5f8d6c203cd9b53e2c95e01037d4">  136</a></span>&#160;<a class="code" href="classEigen_1_1MatrixPowerAtomic.html#ac0ec5f8d6c203cd9b53e2c95e01037d4">MatrixPowerAtomic&lt;MatrixType&gt;::MatrixPowerAtomic</a>(<span class="keyword">const</span> MatrixType&amp; T, RealScalar p) :</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;  m_A(T), m_p(p)</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;{</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  eigen_assert(T.rows() == T.cols());</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  eigen_assert(p &gt; -1 &amp;&amp; p &lt; 1);</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;}</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160; </div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00144"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerAtomic.html#ac3cdfb54a5b60079d068784534cbc174">  144</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixPowerAtomic.html#ac3cdfb54a5b60079d068784534cbc174">MatrixPowerAtomic&lt;MatrixType&gt;::compute</a>(<a class="codeRef" href="../classEigen_1_1Block.html">ResultType</a>&amp; res)<span class="keyword"> const</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  <span class="keywordflow">switch</span> (m_A.rows()) {</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="keywordflow">case</span> 0:</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;      res(0,0) = pow(m_A(0,0), m_p);</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    <span class="keywordflow">case</span> 2:</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;      compute2x2(res, m_p);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    <span class="keywordflow">default</span>:</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;      computeBig(res);</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  }</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;}</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160; </div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixPowerAtomic.html">MatrixPowerAtomic&lt;MatrixType&gt;::computePade</a>(<span class="keywordtype">int</span> degree, <span class="keyword">const</span> MatrixType&amp; IminusT, ResultType&amp; res)<span class="keyword"> const</span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  <span class="keywordtype">int</span> i = 2*degree;</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  res = (m_p-RealScalar(degree)) / RealScalar(2*i-2) * IminusT;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160; </div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keywordflow">for</span> (--i; i; --i) {</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    res = (MatrixType::Identity(IminusT.rows(), IminusT.cols()) + res).<span class="keyword">template</span> triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;        .solve((i==1 ? -m_p : i&amp;1 ? (-m_p-RealScalar(i/2))/RealScalar(2*i) : (m_p-RealScalar(i/2))/RealScalar(2*i-2)) * IminusT).eval();</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  res += MatrixType::Identity(IminusT.rows(), IminusT.cols());</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;}</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160; </div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="comment">// This function assumes that res has the correct size (see bug 614)</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="keywordtype">void</span> MatrixPowerAtomic&lt;MatrixType&gt;::compute2x2(ResultType&amp; res, RealScalar p)<span class="keyword"> const</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;  res.coeffRef(0,0) = pow(m_A.coeff(0,0), p);</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160; </div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  <span class="keywordflow">for</span> (<a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=1; i &lt; m_A.cols(); ++i) {</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    res.coeffRef(i,i) = pow(m_A.coeff(i,i), p);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    <span class="keywordflow">if</span> (m_A.coeff(i-1,i-1) == m_A.coeff(i,i))</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;      res.coeffRef(i-1,i) = p * pow(m_A.coeff(i,i), p-1);</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (2*<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_A.coeff(i-1,i-1)) &lt; <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_A.coeff(i,i)) || 2*<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_A.coeff(i,i)) &lt; <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_A.coeff(i-1,i-1)))</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;      res.coeffRef(i-1,i) = (res.coeff(i,i)-res.coeff(i-1,i-1)) / (m_A.coeff(i,i)-m_A.coeff(i-1,i-1));</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;      res.coeffRef(i-1,i) = computeSuperDiag(m_A.coeff(i,i), m_A.coeff(i-1,i-1), p);</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    res.coeffRef(i-1,i) *= m_A.coeff(i-1,i);</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  }</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;}</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160; </div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="keywordtype">void</span> MatrixPowerAtomic&lt;MatrixType&gt;::computeBig(ResultType&amp; res)<span class="keyword"> const</span></div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  <span class="keyword">using</span> std::ldexp;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> digits = std::numeric_limits&lt;RealScalar&gt;::digits;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  <span class="keyword">const</span> RealScalar maxNormForPade = RealScalar(</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;                                    digits &lt;=  24? 4.3386528e-1L                            <span class="comment">// single precision</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;                                  : digits &lt;=  53? 2.789358995219730e-1L                    <span class="comment">// double precision</span></div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;                                  : digits &lt;=  64? 2.4471944416607995472e-1L                <span class="comment">// extended precision</span></div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;                                  : digits &lt;= 106? 1.1016843812851143391275867258512e-1L    <span class="comment">// double-double</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;                                  :                9.134603732914548552537150753385375e-2L); <span class="comment">// quadruple precision</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;  MatrixType IminusT, sqrtT, T = m_A.template triangularView&lt;Upper&gt;();</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  RealScalar normIminusT;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  <span class="keywordtype">int</span> degree, degree2, numberOfSquareRoots = 0;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  <span class="keywordtype">bool</span> hasExtraSquareRoot = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160; </div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;  <span class="keywordflow">for</span> (<a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=0; i &lt; m_A.cols(); ++i)</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    eigen_assert(m_A(i,i) != RealScalar(0));</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160; </div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    IminusT = MatrixType::Identity(m_A.rows(), m_A.cols()) - T;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    normIminusT = IminusT.cwiseAbs().colwise().sum().maxCoeff();</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="keywordflow">if</span> (normIminusT &lt; maxNormForPade) {</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;      degree = getPadeDegree(normIminusT);</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;      degree2 = getPadeDegree(normIminusT/2);</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;      <span class="keywordflow">if</span> (degree - degree2 &lt;= 1 || hasExtraSquareRoot)</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;        <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;      hasExtraSquareRoot = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    }</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <a class="code" href="group__MatrixFunctions__Module.html#gae51c91f920f6ea4a7f6f72caa1e8249f">matrix_sqrt_triangular</a>(T, sqrtT);</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    T = sqrtT.template triangularView&lt;Upper&gt;();</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    ++numberOfSquareRoots;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  }</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  computePade(degree, IminusT, res);</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  <span class="keywordflow">for</span> (; numberOfSquareRoots; --numberOfSquareRoots) {</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    compute2x2(res, ldexp(m_p, -numberOfSquareRoots));</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    res = res.template triangularView&lt;Upper&gt;() * res;</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  }</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  compute2x2(res, m_p);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;}</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  </div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> MatrixPowerAtomic&lt;MatrixType&gt;::getPadeDegree(<span class="keywordtype">float</span> normIminusT)</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;{</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> maxNormForPade[] = { 2.8064004e-1f <span class="comment">/* degree = 3 */</span> , 4.3386528e-1f };</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;  <span class="keywordtype">int</span> degree = 3;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;  <span class="keywordflow">for</span> (; degree &lt;= 4; ++degree)</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    <span class="keywordflow">if</span> (normIminusT &lt;= maxNormForPade[degree - 3])</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  <span class="keywordflow">return</span> degree;</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;}</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160; </div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> MatrixPowerAtomic&lt;MatrixType&gt;::getPadeDegree(<span class="keywordtype">double</span> normIminusT)</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;{</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">double</span> maxNormForPade[] = { 1.884160592658218e-2 <span class="comment">/* degree = 3 */</span> , 6.038881904059573e-2, 1.239917516308172e-1,</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;      1.999045567181744e-1, 2.789358995219730e-1 };</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  <span class="keywordtype">int</span> degree = 3;</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;  <span class="keywordflow">for</span> (; degree &lt;= 7; ++degree)</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    <span class="keywordflow">if</span> (normIminusT &lt;= maxNormForPade[degree - 3])</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;  <span class="keywordflow">return</span> degree;</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;}</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160; </div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">int</span> MatrixPowerAtomic&lt;MatrixType&gt;::getPadeDegree(<span class="keywordtype">long</span> <span class="keywordtype">double</span> normIminusT)</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;{</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;<span class="preprocessor">#if   LDBL_MANT_DIG == 53</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> maxPadeDegree = 7;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">double</span> maxNormForPade[] = { 1.884160592658218e-2L <span class="comment">/* degree = 3 */</span> , 6.038881904059573e-2L, 1.239917516308172e-1L,</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;      1.999045567181744e-1L, 2.789358995219730e-1L };</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;<span class="preprocessor">#elif LDBL_MANT_DIG &lt;= 64</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> maxPadeDegree = 8;</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> maxNormForPade[] = { 6.3854693117491799460e-3L <span class="comment">/* degree = 3 */</span> , 2.6394893435456973676e-2L,</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;      6.4216043030404063729e-2L, 1.1701165502926694307e-1L, 1.7904284231268670284e-1L, 2.4471944416607995472e-1L };</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;<span class="preprocessor">#elif LDBL_MANT_DIG &lt;= 106</span></div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> maxPadeDegree = 10;</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">double</span> maxNormForPade[] = { 1.0007161601787493236741409687186e-4L <span class="comment">/* degree = 3 */</span> ,</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;      1.0007161601787493236741409687186e-3L, 4.7069769360887572939882574746264e-3L, 1.3220386624169159689406653101695e-2L,</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;      2.8063482381631737920612944054906e-2L, 4.9625993951953473052385361085058e-2L, 7.7367040706027886224557538328171e-2L,</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;      1.1016843812851143391275867258512e-1L };</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> maxPadeDegree = 10;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">double</span> maxNormForPade[] = { 5.524506147036624377378713555116378e-5L <span class="comment">/* degree = 3 */</span> ,</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;      6.640600568157479679823602193345995e-4L, 3.227716520106894279249709728084626e-3L,</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;      9.619593944683432960546978734646284e-3L, 2.134595382433742403911124458161147e-2L,</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;      3.908166513900489428442993794761185e-2L, 6.266780814639442865832535460550138e-2L,</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;      9.134603732914548552537150753385375e-2L };</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  <span class="keywordtype">int</span> degree = 3;</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  <span class="keywordflow">for</span> (; degree &lt;= maxPadeDegree; ++degree)</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    <span class="keywordflow">if</span> (normIminusT &lt;= maxNormForPade[degree - 3])</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  <span class="keywordflow">return</span> degree;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;}</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160; </div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> MatrixPowerAtomic&lt;MatrixType&gt;::ComplexScalar</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;MatrixPowerAtomic&lt;MatrixType&gt;::computeSuperDiag(<span class="keyword">const</span> ComplexScalar&amp; curr, <span class="keyword">const</span> ComplexScalar&amp; prev, RealScalar p)</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;{</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;  <span class="keyword">using</span> std::ceil;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  <span class="keyword">using</span> std::exp;</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;  <span class="keyword">using</span> std::log;</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  <span class="keyword">using</span> std::sinh;</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160; </div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  ComplexScalar logCurr = <a class="codeRef" href="../namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(curr);</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  ComplexScalar logPrev = <a class="codeRef" href="../namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(prev);</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  RealScalar unwindingNumber = <a class="codeRef" href="../namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">ceil</a>((numext::imag(logCurr - logPrev) - RealScalar(EIGEN_PI)) / RealScalar(2*EIGEN_PI));</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;  ComplexScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2) + ComplexScalar(0, RealScalar(EIGEN_PI)*unwindingNumber);</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  <span class="keywordflow">return</span> RealScalar(2) * <a class="codeRef" href="../namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a>(RealScalar(0.5) * p * (logCurr + logPrev)) * <a class="codeRef" href="../namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">sinh</a>(p * w) / (curr - prev);</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;}</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160; </div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> MatrixPowerAtomic&lt;MatrixType&gt;::RealScalar</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;MatrixPowerAtomic&lt;MatrixType&gt;::computeSuperDiag(RealScalar curr, RealScalar prev, RealScalar p)</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;{</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;  <span class="keyword">using</span> std::exp;</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  <span class="keyword">using</span> std::log;</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  <span class="keyword">using</span> std::sinh;</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160; </div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  RealScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2);</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  <span class="keywordflow">return</span> 2 * <a class="codeRef" href="../namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a>(p * (<a class="codeRef" href="../namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(curr) + <a class="codeRef" href="../namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(prev)) / 2) * <a class="codeRef" href="../namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">sinh</a>(p * w) / (curr - prev);</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;}</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160; </div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00339"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPower.html">  339</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixPower.html">MatrixPower</a> : internal::noncopyable</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;{</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160; </div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00354"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPower.html#a5eb445525601510413b53cd347c44716">  354</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1MatrixPower.html#a5eb445525601510413b53cd347c44716">MatrixPower</a>(<span class="keyword">const</span> MatrixType&amp; A) :</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;      m_A(A),</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;      m_conditionNumber(0),</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;      m_rank(A.cols()),</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;      m_nulls(0)</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    { eigen_assert(A.rows() == A.cols()); }</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160; </div>
<div class="line"><a name="l00368"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPower.html#a2ad22d156b1a7ff12d6c40a093cd95eb">  368</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixPowerParenthesesReturnValue.html">MatrixPowerParenthesesReturnValue&lt;MatrixType&gt;</a> <a class="code" href="classEigen_1_1MatrixPower.html#a2ad22d156b1a7ff12d6c40a093cd95eb">operator()</a>(RealScalar p)</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;    { <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1MatrixPowerParenthesesReturnValue.html">MatrixPowerParenthesesReturnValue&lt;MatrixType&gt;</a>(*<span class="keyword">this</span>, p); }</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160; </div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixPower.html#aa1258393dc13acd6e401e000f99b915f">compute</a>(ResultType&amp; res, RealScalar p);</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;    </div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.rows(); }</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.cols(); }</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160; </div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    <span class="keyword">typedef</span> std::complex&lt;RealScalar&gt; ComplexScalar;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    <span class="keyword">typedef</span> Matrix&lt;ComplexScalar, <a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>, <a class="codeRef" href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>, 0,</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;              MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime&gt; ComplexMatrix;</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160; </div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    <span class="keyword">typename</span> MatrixType::Nested m_A;</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160; </div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    MatrixType m_tmp;</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160; </div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    ComplexMatrix m_T, m_U;</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    </div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    ComplexMatrix m_fT;</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160; </div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;    RealScalar m_conditionNumber;</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160; </div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m_rank;</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;    </div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m_nulls;</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160; </div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;    <span class="keywordtype">void</span> split(RealScalar&amp; p, RealScalar&amp; intpart);</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160; </div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;    <span class="keywordtype">void</span> initialize();</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160; </div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;    <span class="keywordtype">void</span> computeIntPower(ResultType&amp; res, RealScalar p);</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160; </div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    <span class="keywordtype">void</span> computeFracPower(ResultType&amp; res, RealScalar p);</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160; </div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;    <span class="keyword">template</span>&lt;<span class="keywordtype">int</span> Rows, <span class="keywordtype">int</span> Cols, <span class="keywordtype">int</span> Options, <span class="keywordtype">int</span> MaxRows, <span class="keywordtype">int</span> MaxCols&gt;</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">void</span> revertSchur(</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;        Matrix&lt;ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols&gt;&amp; res,</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;        <span class="keyword">const</span> ComplexMatrix&amp; T,</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;        <span class="keyword">const</span> ComplexMatrix&amp; U);</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160; </div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    <span class="keyword">template</span>&lt;<span class="keywordtype">int</span> Rows, <span class="keywordtype">int</span> Cols, <span class="keywordtype">int</span> Options, <span class="keywordtype">int</span> MaxRows, <span class="keywordtype">int</span> MaxCols&gt;</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">void</span> revertSchur(</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;        Matrix&lt;RealScalar, Rows, Cols, Options, MaxRows, MaxCols&gt;&amp; res,</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;        <span class="keyword">const</span> ComplexMatrix&amp; T,</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;        <span class="keyword">const</span> ComplexMatrix&amp; U);</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;};</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160; </div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00450"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPower.html#aa1258393dc13acd6e401e000f99b915f">  450</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixPower.html#aa1258393dc13acd6e401e000f99b915f">MatrixPower&lt;MatrixType&gt;::compute</a>(ResultType&amp; res, RealScalar p)</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;{</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;  <span class="keywordflow">switch</span> (cols()) {</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;    <span class="keywordflow">case</span> 0:</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;    <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;      res(0,0) = pow(m_A.coeff(0,0), p);</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    <span class="keywordflow">default</span>:</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;      RealScalar intpart;</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;      split(p, intpart);</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160; </div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;      res = MatrixType::Identity(rows(), cols());</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;      computeIntPower(res, intpart);</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;      <span class="keywordflow">if</span> (p) computeFracPower(res, p);</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;  }</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;}</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160; </div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixPower.html">MatrixPower&lt;MatrixType&gt;::split</a>(RealScalar&amp; p, RealScalar&amp; intpart)</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;{</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;  <span class="keyword">using</span> std::floor;</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160; </div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  intpart = <a class="codeRef" href="../namespaceEigen.html#abf03d773a87830bc7fde51bcd94c89a0">floor</a>(p);</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;  p -= intpart;</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160; </div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  <span class="comment">// Perform Schur decomposition if it is not yet performed and the power is</span></div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  <span class="comment">// not an integer.</span></div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;  <span class="keywordflow">if</span> (!m_conditionNumber &amp;&amp; p)</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    initialize();</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160; </div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;  <span class="comment">// Choose the more stable of intpart = floor(p) and intpart = ceil(p).</span></div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;  <span class="keywordflow">if</span> (p &gt; RealScalar(0.5) &amp;&amp; p &gt; (1-p) * pow(m_conditionNumber, p)) {</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;    --p;</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    ++intpart;</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;  }</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;}</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160; </div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;<span class="keywordtype">void</span> MatrixPower&lt;MatrixType&gt;::initialize()</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;{</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;  <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1ComplexSchur.html">ComplexSchur&lt;MatrixType&gt;</a> schurOfA(m_A);</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;  JacobiRotation&lt;ComplexScalar&gt; rot;</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;  ComplexScalar eigenvalue;</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160; </div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;  m_fT.resizeLike(m_A);</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;  m_T = schurOfA.matrixT();</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;  m_U = schurOfA.matrixU();</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;  m_conditionNumber = m_T.diagonal().array().abs().maxCoeff() / m_T.diagonal().array().abs().minCoeff();</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160; </div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;  <span class="comment">// Move zero eigenvalues to the bottom right corner.</span></div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;  <span class="keywordflow">for</span> (<a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = cols()-1; i&gt;=0; --i) {</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;    <span class="keywordflow">if</span> (m_rank &lt;= 2)</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;      <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;    <span class="keywordflow">if</span> (m_T.coeff(i,i) == RealScalar(0)) {</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;      <span class="keywordflow">for</span> (<a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j=i+1; j &lt; m_rank; ++j) {</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;        eigenvalue = m_T.coeff(j,j);</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;        rot.makeGivens(m_T.coeff(j-1,j), eigenvalue);</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;        m_T.applyOnTheRight(j-1, j, rot);</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;        m_T.applyOnTheLeft(j-1, j, rot.adjoint());</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;        m_T.coeffRef(j-1,j-1) = eigenvalue;</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;        m_T.coeffRef(j,j) = RealScalar(0);</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;        m_U.applyOnTheRight(j-1, j, rot);</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;      }</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;      --m_rank;</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;    }</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;  }</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160; </div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  m_nulls = rows() - m_rank;</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;  <span class="keywordflow">if</span> (m_nulls) {</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;    eigen_assert(m_T.bottomRightCorner(m_nulls, m_nulls).isZero()</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;        &amp;&amp; <span class="stringliteral">&quot;Base of matrix power should be invertible or with a semisimple zero eigenvalue.&quot;</span>);</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;    m_fT.bottomRows(m_nulls).fill(RealScalar(0));</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;  }</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;}</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160; </div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;<span class="keywordtype">void</span> MatrixPower&lt;MatrixType&gt;::computeIntPower(ResultType&amp; res, RealScalar p)</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;{</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;  <span class="keyword">using</span> std::fmod;</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;  RealScalar pp = <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(p);</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160; </div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;  <span class="keywordflow">if</span> (p&lt;0) </div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;    m_tmp = m_A.inverse();</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;  <span class="keywordflow">else</span>     </div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;    m_tmp = m_A;</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160; </div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;  <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;    <span class="keywordflow">if</span> (fmod(pp, 2) &gt;= 1)</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;      res = m_tmp * res;</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;    pp /= 2;</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;    <span class="keywordflow">if</span> (pp &lt; 1)</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    m_tmp *= m_tmp;</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;  }</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;}</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160; </div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;<span class="keywordtype">void</span> MatrixPower&lt;MatrixType&gt;::computeFracPower(ResultType&amp; res, RealScalar p)</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;{</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;  Block&lt;ComplexMatrix,Dynamic,Dynamic&gt; blockTp(m_fT, 0, 0, m_rank, m_rank);</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;  eigen_assert(m_conditionNumber);</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;  eigen_assert(m_rank + m_nulls == rows());</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160; </div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;  MatrixPowerAtomic&lt;ComplexMatrix&gt;(m_T.topLeftCorner(m_rank, m_rank), p).compute(blockTp);</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;  <span class="keywordflow">if</span> (m_nulls) {</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;    m_fT.topRightCorner(m_rank, m_nulls) = m_T.topLeftCorner(m_rank, m_rank).template triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;        .solve(blockTp * m_T.topRightCorner(m_rank, m_nulls));</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;  }</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;  revertSchur(m_tmp, m_fT, m_U);</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;  res = m_tmp * res;</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;}</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160; </div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> Rows, <span class="keywordtype">int</span> Cols, <span class="keywordtype">int</span> Options, <span class="keywordtype">int</span> MaxRows, <span class="keywordtype">int</span> MaxCols&gt;</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> MatrixPower&lt;MatrixType&gt;::revertSchur(</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;    Matrix&lt;ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols&gt;&amp; res,</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;    <span class="keyword">const</span> ComplexMatrix&amp; T,</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;    <span class="keyword">const</span> ComplexMatrix&amp; U)</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;{ res.noalias() = U * (T.template triangularView&lt;Upper&gt;() * U.adjoint()); }</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160; </div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> Rows, <span class="keywordtype">int</span> Cols, <span class="keywordtype">int</span> Options, <span class="keywordtype">int</span> MaxRows, <span class="keywordtype">int</span> MaxCols&gt;</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span> MatrixPower&lt;MatrixType&gt;::revertSchur(</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;    Matrix&lt;RealScalar, Rows, Cols, Options, MaxRows, MaxCols&gt;&amp; res,</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;    <span class="keyword">const</span> ComplexMatrix&amp; T,</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;    <span class="keyword">const</span> ComplexMatrix&amp; U)</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;{ res.noalias() = (U * (T.template triangularView&lt;Upper&gt;() * U.adjoint())).real(); }</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160; </div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00598"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerReturnValue.html">  598</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixPowerReturnValue.html">MatrixPowerReturnValue</a> : <span class="keyword">public</span> ReturnByValue&lt; MatrixPowerReturnValue&lt;Derived&gt; &gt;</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;{</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject PlainObject;</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::RealScalar RealScalar;</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160; </div>
<div class="line"><a name="l00610"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerReturnValue.html#a3067e09b352f967a23bb2a9c50afee88">  610</a></span>&#160;    <a class="code" href="classEigen_1_1MatrixPowerReturnValue.html#a3067e09b352f967a23bb2a9c50afee88">MatrixPowerReturnValue</a>(<span class="keyword">const</span> Derived&amp; A, RealScalar p) : m_A(A), m_p(p)</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;    { }</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160; </div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00620"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixPowerReturnValue.html#a5f15ad16576debad4d4cc0798ff63172">  620</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixPowerReturnValue.html#a5f15ad16576debad4d4cc0798ff63172">evalTo</a>(ResultType&amp; result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;<span class="keyword">    </span>{ <a class="code" href="classEigen_1_1MatrixPower.html">MatrixPower&lt;PlainObject&gt;</a>(m_A.eval()).<a class="code" href="classEigen_1_1MatrixPower.html#aa1258393dc13acd6e401e000f99b915f">compute</a>(result, m_p); }</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160; </div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.rows(); }</div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.cols(); }</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160; </div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;    <span class="keyword">const</span> Derived&amp; m_A;</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;    <span class="keyword">const</span> RealScalar m_p;</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;};</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160; </div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00645"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixComplexPowerReturnValue.html">  645</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixComplexPowerReturnValue.html">MatrixComplexPowerReturnValue</a> : <span class="keyword">public</span> ReturnByValue&lt; MatrixComplexPowerReturnValue&lt;Derived&gt; &gt;</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;{</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject PlainObject;</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> std::complex&lt;typename Derived::RealScalar&gt; ComplexScalar;</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160; </div>
<div class="line"><a name="l00657"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixComplexPowerReturnValue.html#a3e5903e22f70e9deb07c3967ae52fd54">  657</a></span>&#160;    <a class="code" href="classEigen_1_1MatrixComplexPowerReturnValue.html#a3e5903e22f70e9deb07c3967ae52fd54">MatrixComplexPowerReturnValue</a>(<span class="keyword">const</span> Derived&amp; A, <span class="keyword">const</span> ComplexScalar&amp; p) : m_A(A), m_p(p)</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;    { }</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160; </div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00670"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixComplexPowerReturnValue.html#ac7a7947bc6cad6554d31b08b847bc6dd">  670</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixComplexPowerReturnValue.html#ac7a7947bc6cad6554d31b08b847bc6dd">evalTo</a>(ResultType&amp; result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;<span class="keyword">    </span>{ result = (m_p * m_A.log()).<a class="codeRef" href="../namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a>(); }</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160; </div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.rows(); }</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.cols(); }</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160; </div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;    <span class="keyword">const</span> Derived&amp; m_A;</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;    <span class="keyword">const</span> ComplexScalar m_p;</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;};</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160; </div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160; </div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixPowerType&gt;</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;<span class="keyword">struct </span>traits&lt; MatrixPowerParenthesesReturnValue&lt;MatrixPowerType&gt; &gt;</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;{ <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixPowerType::PlainObject ReturnType; };</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160; </div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;<span class="keyword">struct </span>traits&lt; MatrixPowerReturnValue&lt;Derived&gt; &gt;</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;{ <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject ReturnType; };</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160; </div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;<span class="keyword">struct </span>traits&lt; MatrixComplexPowerReturnValue&lt;Derived&gt; &gt;</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;{ <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject ReturnType; };</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160; </div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;}</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160; </div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;<span class="keyword">const</span> MatrixPowerReturnValue&lt;Derived&gt; <a class="codeRef" href="../classEigen_1_1MatrixBase.html#a7ae6c25e6a94a60e147741e76203a73b">MatrixBase&lt;Derived&gt;::pow</a>(<span class="keyword">const</span> RealScalar&amp; p)<span class="keyword"> const</span></div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;<span class="keyword"></span>{ <span class="keywordflow">return</span> MatrixPowerReturnValue&lt;Derived&gt;(derived(), p); }</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160; </div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;<span class="keyword">const</span> MatrixComplexPowerReturnValue&lt;Derived&gt; <a class="codeRef" href="../classEigen_1_1MatrixBase.html#a7ae6c25e6a94a60e147741e76203a73b">MatrixBase&lt;Derived&gt;::pow</a>(<span class="keyword">const</span> std::complex&lt;RealScalar&gt;&amp; p)<span class="keyword"> const</span></div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;<span class="keyword"></span>{ <span class="keywordflow">return</span> MatrixComplexPowerReturnValue&lt;Derived&gt;(derived(), p); }</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160; </div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;} <span class="comment">// namespace Eigen</span></div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160; </div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_MATRIX_POWER</span></div>
<div class="ttc" id="aclassEigen_1_1Block_html"><div class="ttname"><a href="../classEigen_1_1Block.html">Eigen::Block</a></div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html"><div class="ttname"><a href="../classEigen_1_1ComplexSchur.html">ComplexSchur&lt; MatrixType &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a7ae6c25e6a94a60e147741e76203a73b"><div class="ttname"><a href="../classEigen_1_1MatrixBase.html#a7ae6c25e6a94a60e147741e76203a73b">Eigen::MatrixBase::pow</a></div><div class="ttdeci">const MatrixPowerReturnValue&lt; Derived &gt; pow(const RealScalar &amp;p) const</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:698</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixComplexPowerReturnValue_html"><div class="ttname"><a href="classEigen_1_1MatrixComplexPowerReturnValue.html">Eigen::MatrixComplexPowerReturnValue</a></div><div class="ttdoc">Proxy for the matrix power of some matrix (expression).</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:646</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixComplexPowerReturnValue_html_a3e5903e22f70e9deb07c3967ae52fd54"><div class="ttname"><a href="classEigen_1_1MatrixComplexPowerReturnValue.html#a3e5903e22f70e9deb07c3967ae52fd54">Eigen::MatrixComplexPowerReturnValue::MatrixComplexPowerReturnValue</a></div><div class="ttdeci">MatrixComplexPowerReturnValue(const Derived &amp;A, const ComplexScalar &amp;p)</div><div class="ttdoc">Constructor.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:657</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixComplexPowerReturnValue_html_ac7a7947bc6cad6554d31b08b847bc6dd"><div class="ttname"><a href="classEigen_1_1MatrixComplexPowerReturnValue.html#ac7a7947bc6cad6554d31b08b847bc6dd">Eigen::MatrixComplexPowerReturnValue::evalTo</a></div><div class="ttdeci">void evalTo(ResultType &amp;result) const</div><div class="ttdoc">Compute the matrix power.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:670</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerAtomic_html"><div class="ttname"><a href="classEigen_1_1MatrixPowerAtomic.html">Eigen::MatrixPowerAtomic</a></div><div class="ttdoc">Class for computing matrix powers.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:89</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerAtomic_html_ac0ec5f8d6c203cd9b53e2c95e01037d4"><div class="ttname"><a href="classEigen_1_1MatrixPowerAtomic.html#ac0ec5f8d6c203cd9b53e2c95e01037d4">Eigen::MatrixPowerAtomic::MatrixPowerAtomic</a></div><div class="ttdeci">MatrixPowerAtomic(const MatrixType &amp;T, RealScalar p)</div><div class="ttdoc">Constructor.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:136</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerAtomic_html_ac3cdfb54a5b60079d068784534cbc174"><div class="ttname"><a href="classEigen_1_1MatrixPowerAtomic.html#ac3cdfb54a5b60079d068784534cbc174">Eigen::MatrixPowerAtomic::compute</a></div><div class="ttdeci">void compute(ResultType &amp;res) const</div><div class="ttdoc">Compute the matrix power.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:144</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerParenthesesReturnValue_html"><div class="ttname"><a href="classEigen_1_1MatrixPowerParenthesesReturnValue.html">Eigen::MatrixPowerParenthesesReturnValue</a></div><div class="ttdoc">Proxy for the matrix power of some matrix.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:42</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerParenthesesReturnValue_html_ae3a02d943a31427a6dc8c1f60f3367d7"><div class="ttname"><a href="classEigen_1_1MatrixPowerParenthesesReturnValue.html#ae3a02d943a31427a6dc8c1f60f3367d7">Eigen::MatrixPowerParenthesesReturnValue::MatrixPowerParenthesesReturnValue</a></div><div class="ttdeci">MatrixPowerParenthesesReturnValue(MatrixPower&lt; MatrixType &gt; &amp;pow, RealScalar p)</div><div class="ttdoc">Constructor.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerParenthesesReturnValue_html_af91430ff248b714158cfba4301cc0e2b"><div class="ttname"><a href="classEigen_1_1MatrixPowerParenthesesReturnValue.html#af91430ff248b714158cfba4301cc0e2b">Eigen::MatrixPowerParenthesesReturnValue::evalTo</a></div><div class="ttdeci">void evalTo(ResultType &amp;result) const</div><div class="ttdoc">Compute the matrix power.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:61</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerReturnValue_html"><div class="ttname"><a href="classEigen_1_1MatrixPowerReturnValue.html">Eigen::MatrixPowerReturnValue</a></div><div class="ttdoc">Proxy for the matrix power of some matrix (expression).</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:599</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerReturnValue_html_a3067e09b352f967a23bb2a9c50afee88"><div class="ttname"><a href="classEigen_1_1MatrixPowerReturnValue.html#a3067e09b352f967a23bb2a9c50afee88">Eigen::MatrixPowerReturnValue::MatrixPowerReturnValue</a></div><div class="ttdeci">MatrixPowerReturnValue(const Derived &amp;A, RealScalar p)</div><div class="ttdoc">Constructor.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:610</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPowerReturnValue_html_a5f15ad16576debad4d4cc0798ff63172"><div class="ttname"><a href="classEigen_1_1MatrixPowerReturnValue.html#a5f15ad16576debad4d4cc0798ff63172">Eigen::MatrixPowerReturnValue::evalTo</a></div><div class="ttdeci">void evalTo(ResultType &amp;result) const</div><div class="ttdoc">Compute the matrix power.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:620</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPower_html"><div class="ttname"><a href="classEigen_1_1MatrixPower.html">Eigen::MatrixPower</a></div><div class="ttdoc">Class for computing matrix powers.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:340</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPower_html_a2ad22d156b1a7ff12d6c40a093cd95eb"><div class="ttname"><a href="classEigen_1_1MatrixPower.html#a2ad22d156b1a7ff12d6c40a093cd95eb">Eigen::MatrixPower::operator()</a></div><div class="ttdeci">const MatrixPowerParenthesesReturnValue&lt; MatrixType &gt; operator()(RealScalar p)</div><div class="ttdoc">Returns the matrix power.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:368</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPower_html_a5eb445525601510413b53cd347c44716"><div class="ttname"><a href="classEigen_1_1MatrixPower.html#a5eb445525601510413b53cd347c44716">Eigen::MatrixPower::MatrixPower</a></div><div class="ttdeci">MatrixPower(const MatrixType &amp;A)</div><div class="ttdoc">Constructor.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:354</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixPower_html_aa1258393dc13acd6e401e000f99b915f"><div class="ttname"><a href="classEigen_1_1MatrixPower.html#aa1258393dc13acd6e401e000f99b915f">Eigen::MatrixPower::compute</a></div><div class="ttdeci">void compute(ResultType &amp;res, RealScalar p)</div><div class="ttdoc">Compute the matrix power.</div><div class="ttdef"><b>Definition:</b> MatrixPower.h:450</div></div>
<div class="ttc" id="agroup__MatrixFunctions__Module_html_gae51c91f920f6ea4a7f6f72caa1e8249f"><div class="ttname"><a href="group__MatrixFunctions__Module.html#gae51c91f920f6ea4a7f6f72caa1e8249f">Eigen::matrix_sqrt_triangular</a></div><div class="ttdeci">void matrix_sqrt_triangular(const MatrixType &amp;arg, ResultType &amp;result)</div><div class="ttdoc">Compute matrix square root of triangular matrix.</div><div class="ttdef"><b>Definition:</b> MatrixSquareRoot.h:206</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div></div>
<div class="ttc" id="anamespaceEigen_html_aa73e38be0689a463ae14141b9cf89c35"><div class="ttname"><a href="../namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">Eigen::ceil</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_ceil_op&lt; typename Derived::Scalar &gt;, const Derived &gt; ceil(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_abf03d773a87830bc7fde51bcd94c89a0"><div class="ttname"><a href="../namespaceEigen.html#abf03d773a87830bc7fde51bcd94c89a0">Eigen::floor</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_floor_op&lt; typename Derived::Scalar &gt;, const Derived &gt; floor(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="../namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae491aecf7dab66ac7e11008c5766694d"><div class="ttname"><a href="../namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">Eigen::exp</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_exp_op&lt; typename Derived::Scalar &gt;, const Derived &gt; exp(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae8bb75ba4f5f30a7571146dbfa653c6d"><div class="ttname"><a href="../namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">Eigen::log</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af284ce359b6efd4b594a9f8a1f5e5d96"><div class="ttname"><a href="../namespaceEigen.html#af284ce359b6efd4b594a9f8a1f5e5d96">Eigen::sinh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sinh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sinh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
  <ul>
    <li class="navelem"><a class="el" href="dir_8d80078a9d0677ffcc4e95dc0faac368.html">unsupported</a></li><li class="navelem"><a class="el" href="dir_146d0efcf5acec477a223a5f4dae5578.html">Eigen</a></li><li class="navelem"><a class="el" href="dir_32cf1c807a6a54b74f3595d5e0573479.html">src</a></li><li class="navelem"><a class="el" href="dir_61fe7d7028d809a87436fb7749332b49.html">MatrixFunctions</a></li><li class="navelem"><b>MatrixPower.h</b></li>
    <li class="footer">Generated on Thu Apr 21 2022 13:07:59 for Eigen-unsupported by
    <a href="http://www.doxygen.org/index.html">
    <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.9.1 </li>
  </ul>
</div>
</body>
</html>
